BayesProp 0.1.0.7

Bayesian A/B testing for proportions

Bayesian A/B Testing for Proportions

A Python package for Bayesian hypothesis testing of success-rate differences in any Bernoulli-like experiment, using analytic and approximate inference methods. Input data can be binary (0/1) or real-valued on (0, 1) — continuous scores are automatically binarized at a configurable threshold. Typical applications include comparing treatments, groups, items, model variants, or any two conditions whose outcomes can be expressed as proportions. Please check out our Getting Started guide for installation and quick examples.

Features

• Effect-size inference for proportions — estimate and test the difference in success rates for both paired and non-paired samples
• Savage–Dickey Bayes Factor — test a point-null hypothesis ($\delta = 0$) without fitting a separate null model
• Posterior of the null & ROPE — quantify the posterior mass inside a Region of Practical Equivalence for nuanced decisions beyond simple reject/accept
• Posterior predictive checks — assess model fit by comparing observed data to data simulated from the posterior
• Bayes Factor Design Analysis (BFDA) — plan sample sizes to reach a target level of evidence before running the experiment
• Sequential / streaming design — update the posterior batch-by-batch as data arrive and stop early once the Bayes factor crosses an upper or lower threshold (SequentialNonPairedBayesPropTest, SequentialPairedBayesPropTest)
• Publication-ready plots — posterior distributions, predictive checks, Savage–Dickey density-ratio plots, BFDA power curves, and sequential BF₁₀ trajectories out of the box

Models

Model	Class	Method	When to use
Non-paired Beta–Bernoulli	NonPairedBayesPropTest	Conjugate Beta posteriors per arm; P(B>A) by quadrature, Δ summaries by Monte Carlo	Independent groups, exact & fast
Paired Logistic (Laplace)	PairedBayesPropTest	MAP + Laplace approximation	Paired scores, large n, fast iteration
Paired Logistic (Pólya–Gamma)	PairedBayesPropTestPG	Exact Gibbs sampling	Paired scores, small n, exact posterior

Quick start

import numpy as np
from bayesprop.resources.bayes_nonpaired import NonPairedBayesPropTest

# Binary or [0,1]-valued data:
y_A = np.array([1,1,0,1,1,0,1,1,1,1,1,1,1,0,1,1,1,0,1,1])     # 16/20 = 0.80
y_B = np.array([0,1,0,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0,0,0])     #  6/20 = 0.30

# Fit posterior & summarise
model = NonPairedBayesPropTest(seed=42).fit(y_A, y_B)

s = model.summary
print(f"\nMean Δ (θ_A − θ_B) = {s.mean_delta:+.4f}")
print(f"95% CI = [{s.ci_95.lower:.4f}, {s.ci_95.upper:.4f}]")
print(f"P(A > B) = {s.p_A_greater_B:.4f}")

# ── Unified decision ─────────────────────────────────────────────────
d = model.decide()
bf = d.bayes_factor

print("\n--- Unified Decision ---")
print(f"  Bayes Factor: BF₁₀ = {bf.BF_10:.2f}  → {bf.decision}")
print(f"  Posterior Null: P(H₀|D) = {d.posterior_null.p_H0:.4f}  → {d.posterior_null.decision}")
print(f"  ROPE: {d.rope.decision} ({d.rope.pct_in_rope:.1%} in ROPE)")

# Plots
model.plot_posteriors()
model.plot_savage_dickey()

Installation

pip install BayesProp

Or with uv:

uv pip install BayesProp

For development (from source):

git clone https://github.com/AVoss84/bayesProp.git
cd bayesprop
uv venv --python 3.13
uv sync
source .venv/bin/activate

Dependencies

• Python ≥ 3.13
• numpy, scipy, matplotlib, pandas
• pydantic (v2)
• polyagamma

References

• Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). Chapman & Hall/CRC.
• Kruschke, J. K. (2018). Rejecting or accepting parameter values in Bayesian estimation. Advances in Methods and Practices in Psychological Science, 1(2), 270–280.
• Polson, N. G., Scott, J. G. & Windle, J. (2013). Bayesian inference for logistic models using Pólya–Gamma latent variables. JASA, 108(504), 1339–1349.
• Schönbrodt, F. D. & Wagenmakers, E.-J. (2018). Bayes factor design analysis: Planning for compelling evidence. Psychonomic Bulletin & Review, 25(1), 128–142.